Geodesic
The Maximum Number of Edges in a Three-Dimensional Grid-Drawing
Journal of Graph Algorithms and Applications, Tome 8 (2004) no. 1, pp. 21-26.

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An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of three-dimensional grid-drawings is obtained as a corollary. Our results generalise to the setting of multi-dimensional polyline grid-drawings. 
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Prosenjit Bose; Jurek Czyzowicz; Pat Morin; David Wood. The Maximum Number of Edges in a Three-Dimensional Grid-Drawing. Journal of Graph Algorithms and Applications, Tome 8 (2004) no. 1, pp. 21-26. doi : 10.7155/jgaa.00079. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00079/

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